Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 1 (2017), 72-89.
Duality for increasing convex functionals with countably many marginal constraints
In this work we derive a convex dual representation for increasing convex functionals on a space of real-valued Borel measurable functions defined on a countable product of metric spaces. Our main assumption is that the functionals fulfill marginal constraints satisfying a certain tightness condition. In the special case where the marginal constraints are given by expectations or maxima of expectations, we obtain linear and sublinear versions of Kantorovich’s transport duality and the recently discovered martingale transport duality on products of countably many metric spaces.
Banach J. Math. Anal., Volume 11, Number 1 (2017), 72-89.
Received: 17 October 2015
Accepted: 18 February 2016
First available in Project Euclid: 10 November 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
Secondary: 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12] 91G20: Derivative securities
Bartl, Daniel; Cheridito, Patrick; Kupper, Michael; Tangpi, Ludovic. Duality for increasing convex functionals with countably many marginal constraints. Banach J. Math. Anal. 11 (2017), no. 1, 72--89. doi:10.1215/17358787-3750133. https://projecteuclid.org/euclid.bjma/1478746987